Sharapova, who won the title in 2008, was at her ruthless best as she overpowered the Argentine in stifling conditions on the Hisense Arena.
It was an impressive display by Sharapova against a player who was once ranked as high as 26 in the world.
The Russian fourth seed also showed no signs of a left ankle injury that forced her to withdraw from the Brisbane International two weeks ago.
Sharapova claimed the first set in just 25 minutes and didn't lose a game until 2-0 in the second set, when her serve temporarily deserted her. But she quickly recovered to break straight back and run away with the match.
Dulko had no answer to the power of Sharapova's ground strokes, her forehand particularly damaging throughout the 58-minute encounter. Sharapova smashed 14 winners past Dulko and forced the Argentine into 22 errors over the two sets.
"I knew I had a tough opponent today," a delighted Sharapova said afterwards. "I focused on every point and took her time away -- she's a player who loves time on the ball."
Sharapova has a relatively easy passage into the third round with her next opponent US qualifier Jamie Hampton.
Ruthless Sharapova demolishes Dulko
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